Question

a baking club wants to form an executive committee. there are $12$ people in the baking club, including mark. in how many ways can the baking club form an executive committee with $4$ people?

Answer 1

To form the executive committee, the baking club needs to select 4 people out of the 12 members. The number of ways to do this is 495.

Step-by-step explanation:

To form the executive committee, the baking club needs to select 4 people out of the 12 members, including Mark. This is a combinations problem, since the order of selection does not matter. The formula to calculate combinations is:

C(n, r) = n! / (r!(n-r)!)

Substituting the values in the formula, we have:

C(12, 4) = 12! / (4!(12-4)!)

Simplifying the expression and calculating, we get:

C(12, 4) = 12! / (4!8!) = 12 * 11 * 10 * 9 / (4 * 3 * 2 * 1)

C(12, 4) = 495

Therefore, the baking club can form an executive committee in 495 ways with 4 people.